My Math Forum Conditional Expectation and Variance Question

 October 26th, 2007, 09:54 PM #1 Newbie   Joined: Oct 2007 Posts: 4 Thanks: 0 Conditional Expectation and Variance Question Here's the question I'm having trouble with: Show Var[E[Y|X]] = 0 given random variables X and Y are independent, keeping in mind Var[Y] = Var[E[Y|X]] + E[Var[Y|X]]. Here's the work I've done so far. 1) Var[E[Y|X]] = E[(E[Y|X])^2] - (E[E[Y|X]])^2 (using Var[X] = E[X^2] - (E[X])^2) 2) Var[E[Y|X]] = E[E[Y|X]^2] - (E[Y])^2 (using E[Y|X] = E[Y] if X, Y are independent) 3) E[Y]^2 - E[Y]^2 (I want to use E[Y] = E[E[Y|X]] and but I need E[E[Y|X]^2] = E[E[Y|X]]^2 What am I missing here? Thanks in advance.
 October 30th, 2007, 01:05 PM #2 Member   Joined: Nov 2006 From: Vancouver, Canada Posts: 46 Thanks: 0 Hmm.. That's a silly question your prof gave. I mean E(Y|X) = E(Y) due to independence, and so E(Y) is just a single number, of course Var(E(Y)) is 0... Did I understand the question wrong?

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